Mathematics : Three Dimensional Geometry

Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is :

• $\frac{35}{\sqrt{34}}$

• $\frac{1}{3\sqrt{34}}$

• $\frac{35}{3\sqrt{34}}$

• $\frac{35}{2\sqrt{34}}$

If the equation 2x² + 7 xy + 3y² - 9 x - 7y + k = 0 represents a pair of lines, then k is equal to

• 4

• 2

• 1

• - 4

The angle between the lines 2x - y + 3 = 0 and x + 2y + 3 = 0 is :

• 90°

• 60°

• 45°

• 30°

Distance between the pair of lines represented by the equation x² - 6xy + 9y² + 3 - 9y - 4 = 0 is:

• $\frac{15}{\sqrt{10}}$

• $\frac{1}{2}$

• $\sqrt{\frac{5}{2}}$

• $\frac{1}{\sqrt{10}}$

The angles of a triangle are in the ratio 1 : 3 : 5. Then the greatest angle is :

• $\frac{5\mathrm{\pi }}{9}$

• $\frac{2\mathrm{\pi }}{9}$

• $\frac{7\mathrm{\pi }}{9}$

• $\frac{11\mathrm{\pi }}{9}$

A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. Then angle subtended by the arc at the centre is:

• 50°

• 210°

• 100°

• 60°

The radius of the circle x² + y² + z² - 2y - 4z - 11 = 0 and x + 2y + 2z - 15 = 0 is :

• $\sqrt{3}$

• $\sqrt{5}$

• $\sqrt{7}$

• 3

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}} = \overrightarrow{0}, \left|\overrightarrow{\mathrm{a}}\right| = 3, \left|\overrightarrow{\mathrm{b}}\right| = 5 \mathrm{and} \left|\overrightarrow{\mathrm{c}}\right| = 7$, then angle between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is :

• 0

• 30°

• 45°

• 60°

The points A (4, 5, 1), B (0, - 1, - 1), C(3, 9, 4) and D(- 4, 4, 4) are

• collinear

• coplanar

• non-coplanar

• non-collinear

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}} = \overrightarrow{0}, \left|\overrightarrow{\mathrm{a}}\right| = 3, \left|\overrightarrow{\mathrm{b}}\right| = 5 \mathrm{and} \left|\overrightarrow{\mathrm{c}}\right| = 7$, then the angle between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is :

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• ${\cos }^{-1}\left(\frac{2}{225}\right)$

• $\frac{\mathrm{\pi }}{4}$